The brain's sensorimotor cortex, as a complex neural sensorimotor control system, inherently finds and accomplishes all of its tasks in an optimal manner in terms of speed, accuracy, and efficiency in a vast range of input conditions [3, 4]. Noises, nonlinearities, delays, uncertainties, and redundancies are among many major problems that a sensorimotor control system may experience [5].
A primate's sensorimotor controller is equipped with the ability to predict motor movements and to compensate for time delays. Time-delay estimation is a difficult problem to simulate because it renders even the simplest linear systems nonlinear; yet, biological control systems are robust enough to deal with time delays. It is unclear, however, how this is achieved in biological systems.
For example, vestibulo-ocular reflex (VOR), a motor control system that stabilizes vision during head movements, is not prone to occurrence of delay up to 10 milliseconds from the onset of stimulus [8]. Smooth pursuit, another efficient visual control system in humans for target tracking in the visual field, has the ability to process information with an 80-130 millisecond delay in the brain [25, 26]. Delays make control difficult because information about the current state of the motor system is outdated. A motor control system that does not have delay compensation mechanisms could not correct for errors, leading to potential inefficiencies and instability.
Currently available time-delay estimation techniques mainly cover linear systems including, for example, constant time delays, random time delay with specific noise characteristics, and restricted dynamic time delay [20-27]. Most biological systems, however, exhibit some degree of variability, nonlinearity, and uncertainty, which can render these methods inapplicable. Further, most delay estimation procedures are not used in the context of predictive control methodology. The Hilbert-Huang Transform-based method, for example, is found to be the most efficient delay estimation technique with a focus on practical applicability to the motor control. However, the process is a complex one [26]. As such, a comprehensive and predictive computational model to explain time-delay compensation in biological control is still lacking.